New algorithms for calculating discrete Fourier transforms
USSR Computational Mathematics and Mathematical Physics
Image Representation Via a Finite Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalised finite radon transform for N x N images
Image and Vision Computing
2-D and 1-D multipaired transforms: frequency-time type wavelets
IEEE Transactions on Signal Processing
Efficient algorithms for computing the 2-D hexagonal Fouriertransforms
IEEE Transactions on Signal Processing
Shifted Fourier transform-based tensor algorithms for the 2-D DCT
IEEE Transactions on Signal Processing
The discrete periodic Radon transform
IEEE Transactions on Signal Processing
Method of paired transforms for reconstruction of images from projections: discrete model
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size NxN was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that ''the original definition by Matus and Flusser was restricted to apply only to square arrays of prime size,'' and ''Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,'' and ''Kingston further extended this to define an FRT that applies to prime-adic arrays''. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size NxN which was published earlier by Artyom Grigoryan in 1984-1991 in the USSR. The above mentioned ''Fourier slice theorem'' repeated the known tensor transform-based algorithm of 2-D DFT [5-11], which was developed for any order N"1xN"2 of the transformation, including the cases of NxN, when N=2^r, (r1), and N=L^r, (r=1), where L is an odd prime. The problem of ''over-representation'' of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6-9].